Paper: arXiv 2511.00781

Authors: Purba Banerjee, Srikanth Iyer, Shashi Jain

Abstract

We consider an investor who wants to hedge a path-dependent option with maturity $T$ using a static hedging portfolio using cash, the underlying, and vanilla put/call options on the same underlying with maturity $ t_1$, where $0 < t_1 < T$. We propose a model-free approach to construct such a portfolio. The framework is inspired by the \textit{primal-dual} Martingale Optimal Transport (MOT) problem, which was pioneered by \cite{beiglbock2013model}. The optimization problem is to determine the portfolio composition that minimizes the expected worst-case hedging error at $t_1$ (that coincides with the maturity of the options that are used in the hedging portfolio). The worst-case scenario corresponds to the distribution that yields the worst possible hedging performance. This formulation leads to a \textit{min-max} problem. We provide a numerical scheme for solving this problem when a finite number of vanilla option prices are available. Numerical results on the hedging performance of this model-free approach when the option prices are generated using a \textit{Black-Scholes} and a \textit{Merton Jump diffusion} model are presented. We also provide theoretical bounds on the hedging error at $T$, the maturity of the target option.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 5.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong theoretical framework extending static option hedging to a robust model-free min-max setup using Martingale Optimal Transport (MOT). While the mathematical derivations and discretization convergence proofs are solid, the empirical validation relies on synthetic data models (Black-Scholes and Merton Jump Diffusion) rather than extensive real-world market datasets.

Research Flowchart

  flowchart TD
    A[Goal: Model-free robust static hedging of path-dependent options at T] --> B[Inputs: Cash, Underlying, Vanilla Options at t1 < T]
    B --> C[Methodology: Primal-Dual Martingale Optimal Transport MOT]
    C --> D[Optimization: Min-Max formulation for worst-case hedging error at t1]
    D --> E[Numerical Scheme: Solve with finite option prices]
    E --> F[Validation & Bounds: Test on Black-Scholes & Merton Jump Diffusion + Error bounds at T]

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